计算不定积分∫arctanxdx\int \arctan x dx∫arctanxdx.
设f(x)=x3+3xlimx→1f(x)f(x) = x^3 + 3x\lim\limits_{x \to 1} f(x)f(x)=x3+3xx→1limf(x)，且limx→1f(x)\lim\limits_{x \to 1} f(x)x→1limf(x)存在，求f(x)f(x)f(x).
计算定积分∫0π42+2cos2xdx\int_{0}^{\dfrac{\pi}{4}} \sqrt{2 + 2\cos2x} dx∫04π2+2cos2xdx.
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